Macaulay's method (the double integration method) is a technique used in structural analysis to determine the deflection of Euler-Bernoulli beams. Use of Macaulay's technique is very convenient for cases of discontinuous and/or discrete loading. Typically partial uniformly distributed loads (u.d.l.) and uniformly varying loads (u.v.l.) over the span and a number of concentrated loads are conveniently handled using this technique.
The first English language description of the method was by Macaulay.[1] The actual approach appears to have been developed by Clebsch in 1862.[2] Macaulay's method has been generalized for Euler-Bernoulli beams with axial compression,[3] to Timoshenko beams,[4] to elastic foundations,[5] and to problems in which the bending and shear stiffness changes discontinuously in a beam.[6]
- ^ W. H. Macaulay, "A note on the deflection of beams", Messenger of Mathematics, 48 (1919), 129.
- ^ J. T. Weissenburger, ‘Integration of discontinuous expressions arising in beam theory’, AIAA
Journal, 2(1) (1964), 106–108.
- ^ W. H. Wittrick, "A generalization of Macaulay’s method with applications in structural mechanics", AIAA Journal, 3(2) (1965), 326–330.
- ^ A. Yavari, S. Sarkani and J. N. Reddy, ‘On nonuniform Euler–Bernoulli and Timoshenko beams with jump discontinuities: application of distribution theory’, International Journal of Solids and Structures, 38(46–7) (2001), 8389–8406.
- ^ A. Yavari, S. Sarkani and J. N. Reddy, ‘Generalised solutions of beams with jump discontinuities
on elastic foundations’, Archive of Applied Mechanics, 71(9) (2001), 625–639.
- ^ Stephen, N. G., (2002), "Macaulay's method for a Timoshenko beam", Int. J. Mech. Engg. Education, 35(4), pp. 286-292.